NTA JEE Main 8th January 2020 Shift 1

A particle is moving along the $$x$$-axis with its coordinate with time $$t$$ given by $$x(t) = 10 + 8t - 3t^2$$. Another particle is moving along the $$y$$-axis with its coordinate as a function of time given by $$y(t) = 5 - 8t^3$$. At $$t = 1$$ s, the speed of the second particle as measured in the frame of the first particle is given as $$\sqrt{v}$$. Then $$v$$ (in m s$$^{-1}$$) is

A body A of mass $$m = 0.1$$ kg has an initial velocity of $$3\hat{i}$$ m s$$^{-1}$$. It collides elastically with another body B of the same mass which has an initial velocity of $$5\hat{j}$$ m s$$^{-1}$$. After the collision, A moves with a velocity $$\vec{v} = 4(\hat{i} + \hat{j})$$ m s$$^{-1}$$. The energy of B after the collision is written as $$\frac{x}{10}$$ J. The value of $$x$$ is

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is __________ Hz.

Four resistances of 15 $$\Omega$$, 12 $$\Omega$$, 4 $$\Omega$$ and 10 $$\Omega$$ respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10 $$\Omega$$ to balance the network is __________ $$\Omega$$.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is

For the Balmer series, in the spectrum of H atom, $$\bar{v} = R_H\left\{\frac{1}{n_1^2} - \frac{1}{n_2^2}\right\}$$, the correct statements among (I) to (IV) are,
(I) As wavelength decreases, the lines in the series converge.
(II) The integer $$n_1$$ is equal to 2.
(III) The lines of the longest wavelength correspond to $$n_2 = 3$$.
(IV) The ionization energy of hydrogen can be calculated from the wave number of these lines.

The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively are:

The third ionization enthalpy is minimum for:

The predominant intermolecular forces present in ethyl acetate, a liquid, are:

The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively: